# Petrial great stellated dodecahedron

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Petrial great stellated dodecahedron | |
---|---|

Rank | 3 |

Type | Regular |

Space | Spherical |

Notation | |

Schläfli symbol | ^{[1]} |

Elements | |

Faces | 6 skew decagons |

Edges | 30 |

Vertices | 20 |

Vertex figure | Triangle |

Related polytopes | |

Regiment | Gissid |

Petrie dual | Great stellated dodecahedron |

Conjugate | Petrial dodecahedron |

Convex hull | Dodecahedron |

Abstract properties | |

Flag count | 120 |

Euler characteristic | -4 |

Schläfli type | {10,3} |

Topological properties | |

Orientable | No |

Genus | 6 |

Properties | |

Convex | No |

The **petrial great stellated dodecahedron** is a regular skew polyhedron and is the Petrie dual of the great stellated dodecahedron, and so it shares both of its vertices and edges with the great stellated dodecahedron. It consists of 6 skew decagrams and has an Euler characteristic of -4.

## Vertex coordinates[edit | edit source]

The vertices of the petrial great stellated dodecahedron are identical to those of the great stellated dodecahedron, which is the regiment colonel.

## Related polyhedra[edit | edit source]

The rectification of the petrial great stellated dodecahedron is the great icosihemidodecahedron, which is uniform.

## External links[edit | edit source]

- Wikipedia Contributors. "Petrie dual".

## References[edit | edit source]

## Bibliography[edit | edit source]

- McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF).
*Discrete Computational Geometry*(47): 449–478. doi:10.1007/PL00009304.